v63-173

8/2/2019 v63-173

1/8

AbstractThis paper presents a study of laminar to turbulenttransition on a profile specifically designed for wind turbine blades,

the DU91-W2-250, which belongs to a class of wind turbine

dedicated airfoils, developed by Delft University of Technology. A

comparison between the experimental behavior of the airfoil studied

at Delft wind tunnel and the numerical predictions of the commercial

CFD solver ANSYS FLUENT has been performed. The prediction

capabilities of the Spalart-Allmaras turbulence model and of the -

Transitional model have been tested. A sensitivity analysis of the

numerical results to the spatial domain discretization has also been

performed using four different computational grids, which have been

created using the mesher GAMBIT.The comparison between experimental measurements and CFD

results have allowed to determine the importance of the numerical

prediction of the laminar to turbulent transition, in order not to

overestimate airfoil friction drag due to a fully turbulent-regime flow

computation.

KeywordsCFD, wind turbine, DU91-W2-250, laminar to

turbulent transition

I. INTRODUCTIONANDBACKGROUNDITH its 2020 goals to increase the share of renewable

energy in the overall energy mix to 20% and to cut

carbon emissions by 20%, the EU is leading the world in termsof renewable energy deployment, exports and promotion.

Today Europe gets approximately 20% of its electricity from

renewable energy sources, including 5.3% from wind Energy.

That share will increase up to 2020 when, under the terms of

the EUs renewable energy directive, which sets legally

binding targets for renewable energy in Europe, 34% of the

EUs total electricity consumption will come from renewable

energy sources, with wind energy accounting for 14% [1]. In

this scenario, the continuous quest for clean energy appears to

be connected with the development of the aerodynamics of

actual wind turbines, in order to achieve a growth of their

performances, both for the classical horizontal-axis (HAWT)

and also the vertical-axis (VAWT) concepts [2].

For the past years, it was common practice to use existing

airfoil families, like the well known NACA series, for the

design of wind turbine blades, however the need of furthering

wind turbine technologies has led to the quest for alternatives.

Marco Raciti Castelli is a Research Associate at the Department of

Industrial Engineering of the University of Padua, Via Venezia 1, 35131

Padua, Italy (e-mail: [email protected]).

Giada Grandi is a M.Sc. student in Aerospace Engineering at the

University of Padua, Via Venezia 1, 35131 Padua, Italy.

Ernesto Benini is Associate Professor at the Department of Industrial

Engineering of the University of Padua, Via Venezia 1, 35131 Padua, Italy (e-mail: [email protected]).

The airfoil analyzed in the present work is the DU91-W2-

250, which belongs to a class of wind turbine dedicated

airfoils developed by Delft University of Technology. At

present, DU airfoils are being used by various wind turbine

manufacturers worldwide,in many different rotor blades.

The design of the DU91-W2-250 airfoil followed wind

tunnel tests on a 25% thick NACA airfoil from the 63-4xx

series, linearly scaled from 21%. To compensate for the

resulting loss in lift of the upper surface, a certain amount of

lower surface aft loading was incorporated, giving DU91-W2-

250 the typical S-shape of the pressureside. This airfoil, likeother 25% thick airfoils, has very high peak lift coefficient in

the smooth condition and presents an acceptable performance

in the rough situation, differently from classical NACA

airfoils. The main features of the mid span airfoil are a good

maximum lift to drag ratio and a smooth stall behavior [3] [4].

Fig.1 Comparison between the DU91-W2-250 airfoil and a 5-digit

NACA airfoil

Every flow causes pressure and friction on the body surface,

which result in forces and moments acting on the body itself.

Nowadays, thanks to advances in numerical methods and

computing power, the investigation and solution of the flow

field around an airfoil has become relatively simple. By

performing CFD analysis on the DU91-W2-250, together withturbulence and transition modeling testing, the main purpose

of the present work is to investigate its behavior, with

particular attention to the laminar to turbulent transition

phenomena.

Lombardi et al. [5] tested the capability of a classical RANS

solver of predicting the friction drag over a NACA 0012

airfoil for 0 deg angle of attack and compared CFD results

with the values given by a coupled potential/boundary-layer

method. The analyzed range of Reynolds numbers varied from

300,000 to 9,000,000. As a result, being the local skin friction

coefficient defined as:

cf= w / (cV2

) (1)

M. Raciti Castelli, G. Grandi and E. Benini

Numerical Analysis of Laminar to Turbulent

Transition on the DU91-W2-250 airfoil

W

World Academy of Science, Engineering and Technology 63 2012

914

8/2/2019 v63-173

2/8

the relative integral over the whole airfoil length resulted

overestimated by all turbulence models - even using highly

refined grids - because of their inherent inability to predict the

boundary layer transition.

Lian and Shyy [6] coupled a Navier-Stokes solver and a

Reynolds-averaged two-equation closure to study laminar toturbulent transition for low Reynolds number flows around a

SD7003 airfoil, obtaining good agreement between numerical

predictions and experimental measurements regarding the

transition location, as well as overall flow structures.

Menter et al. [7], [8] developed the - model, one of the

first transition prediction tools available in a commercial flow

solver, which is compatible with modern CFD approaches.

The model is based on two transport equations, one for

intermittency and one for the transition onset criteria in terms

of momentum thickness Reynolds number. A significant

number of test cases were used to validate the transition model

for turbomachinery and aerodynamic applications, including a

2D horizontal-axis wind turbine airfoil section [8].Benini and Ponza [9] investigated the capability of the -

transition model in predicting the laminar to turbulent

transition in the boundary layer developing around a

supercritical airfoil (NLR 7301). The numerical results showed

a certain degree of sensitivity to the turbulence intensity level

set at the domain inlet, being the transition onset moved

foreward with increasing turbulence levels.

Hosseinverdi and Boroomand tested the capability of two

empirical correlations (Cebeci & Smith and eN

method)

coupled to the two-equation k- SST turbulence model of

Menter, in order to predict the incompressible transitional flow

over a S809 wind turbine airfoil, obtaining significant

improvements in drag prediction by using the transitionalcomputation in comparison with the fully turbulent simulation

[10].

Yuhong and Congming [11] applied a two-equation

transition model to the flow over a wind turbine S814 airfoil.

Numerical predictions were compared with the experimental

data of the National Renewable Energy Laboratory (NREL)

and the simulation results using fully turbulent SST model.

The analysis showed that the transition model can capture the

phenomena of transition and flow separation more effectively.

Under certain working conditions, the transition model

resulted able to predict lift and drag coefficients more

accurately than a full turbulence model.

The main objective of this work is a 2D numericalinvestigation on DU91-W2-250 airfoil, performed to

demonstrate how, using a numerical tool capable to foresee the

laminar to turbulent transition, it is possible to avoid numerical

results being affected by the overestimation of airfoil friction

drag due to a fully turbulent-regime flow computation. The

proposed analysis focuses mainly on three parameters:

aerodynamic coefficients Cl, Cd ; the wall y+ ; skin friction coefficient cf.

The reference values for the considered airfoil derived from

measurements performed at Delft University Low-speed Wind

Tunnel [12] at a Reynolds number of 3.0106, which is typical

for wind turbine applications. In this case, laminar to turbulent

free transition (it is assumed that the smooth surface does not

trigger turbulence until the laminar boundary layer becomes

unstable and the flow experiences free transition to turbulence)

is an important factor to be taken into account. Table I

summarizes the main reference values of the experimental

tests.

TABLEI

MAIN REFERENCE VALUES OF THE EXPERIMENTAL MEASUREMENTS

Denomination Value

Airfoil section DU91-W2-250

c [m] 0.6

Re [-] 3.0106

[deg] 0.49

CFD analysis was performed using both Spalart-Allmaras

turbulence model and - Transitional model. The first one is a

relatively simple one-equation model that solves a modeledtransport equation for the kinematic eddy viscosity; this model

was designed specifically for aerospace applications involving

wall-bounded flows and was shown to give good results for

boundary layers subjected to adverse pressure gradients [13].

The second one is based on the coupling of the SST

transport equations with two other transport equations, one for

the intermittency and one for the transition onset criteria, in

terms of momentum-thickness Reynolds number [7] [8]. Its

main characteristic is, however, the capability of foreseeing

laminar to turbulent transition. In fact, classical turbulence

models, although widely used to calculate the pressure loads

acting on blade profiles, are unable to predict the laminar-

turbulent transition, resulting in poor prediction of rotorperformance, caused by the overestimation of airfoil friction

drag due to a fully turbulent-regime flow computation [14],

especially for high values of the tip speed ratio where, due to

the low range of blade relative angles of attack, the skin

friction contribution to overall airfoil drag is quite relevant

[15].

II.MODEL GEOMETRYThe present work was performed applying both Spalart-

Allmaras turbulence model and - Transitional model to four

different spatial domain discretizations created with the

mesher GAMBIT. The grids were substantially constructed

in the same way, differing from each other by the number oflayers which composed the near-wall discretization. The

computational domain was in fact subdivided in two sub-

domains:

an external portion, comprising the whole simulationdomain;

an internal portion, bounding the area close to theairfoil section. Great attention was directed to this

element: in fact, the most important differences

between the four proposed meshes were concentrated in

it.

A high-quality mesh was created close to the airfoil surface

with the purpose of better capturing the surface boundary layer

and to obtain y+ values close to 1. This parameter is a mesh-


915

8/2/2019 v63-173

3/8

dependent dimensionless distance that quantifies the degree of

wall layer resolution, in formulas:

y+

= (uy) / (2)

Each grid was called as Mod followed by a number from1 to 4. Tables II and III summarize the main features of the

adopted grids, as well as the resulting y+

peak values.

TABLEII

MAIN MESH FEATURES AND Y+ VALUES OBTAINED USING THE SPALART-

ALLMARAS TURBULENCE MODEL

NameFirst row

[mm]

Growth

factor [-]

Rows

[-]

Suction

side

peak y+

value [-]

Pressure

side peak

y+ value

[-]

Mod1 0.7 1.2 4 110 110

Mod2 0.05 1.2 15 7.5 7

Mod3 0.025 1.2 17 3.8 3.5

Mod4 0.0125 1.2 21 1.85 1.8

TABLEIII

MAIN MESH FEATURES AND Y+ VALUES OBTAINED USING THE -

TRANSITIONAL MODEL MODEL

NameFirst row

[mm]

Growth

factor [-]

Rows

[-]

Suction

side

peak y+

value [-]

Pressure

side peak

y+

value

[-]

Mod1 0.7 1.2 4 110 105

Mod2 0.05 1.2 15 8.25 8.5

Mod3 0.025 1.2 17 3.5 3

Mod4 0.0125 1.2 21 1.8 1.6

III. DESCRIPTION OF THE NUMERICAL FLOW FIELDAs already mentioned in the previous section, all the

adopted grids presented common geometric features, except

for the areas close to the airfoil. As the aim of the numerical

simulations was to explore the 2D flow field close to a blade

profile, the computational domain was discretized into two

macro-areas:

a rectangular outer zone, determining the overallcalculation domain, with a circular opening centered at

25% of chord length, which was identified as Wind

Tunnel sub-grid, fixed;

a circular inner zone, which was identified asAirfoil sub-grid, were grid points were clustered in order to obtain an

accurate mesh setup of both the wall boundary layer and

the airfoil wake.

Fig. 2 shows the main dimensions and boundary conditions

of the Wind Tunnel sub-gridarea. The computational domain

width was set to 20 blade chords. In order to allow a full

development of the wake behind the airfoil, inlet and outlet

boundary conditions were placed respectively 10 blade chord

upwind and 20 blade chord downwind with respect to the

airfoil test section.

Two symmetry boundary conditions were used for the two

side walls. The boundary between Wind Tunnel sub-gridand

Airfoil sub-grid was set as an interior, thus ensuring the

continuity of the flow field.

Fig. 2 Main dimensions and boundary conditions of the Wind Tunnel

sub-gridarea

TABLEIV

MAIN REFERENCE VALUES OF THE NUMERICAL FLOW FIELD

Denomination Value

[kg/m3] 1.225

[Pas] 1.789410-5

Vx [m/s] 73

Vy [m/s] 0

IV. DISCRETIZATION OF THE NUMERICAL FLOW FIELDA totally unstructured mesh was chosen for the Wind Tunnel

sub-grid, in order to reduce the engineering time to prepare the

CFD simulations.

Fig. 3Airfoil sub-gridmesh, Mod 1

Fig. 4Airfoil sub-gridmesh, Mod 2


916

8/2/2019 v63-173

4/8

Fig. 5Airfoil sub-grid mesh, Mod 3

Fig. 6 Leading edge details ofAirfoil sub-grid mesh, Mod 3

Fig. 7 Trailing edge details ofAirfoil sub-grid mesh, Mod 3

With regard to the Airfoil sub-grid, the computational grids

around the tested airfoil were constructed from lower

topologies to higher ones, adopting appropriate size functions,

in order to cluster grid points near the leading edge and the

trailing edge of the blade profile, so as to improve the CFD

code capability of determining lift, drag and the laminar to

turbulent transition onset.

A high-quality structured mesh was created close to the

airfoil surface, in order to better capture the boundary layer,

while outside the boundary layer region a triangular

unstructured grid was created using proper size functions.

Figs. from 3 to 8 show the main features of the computational

grids around the tested airfoil for the four candidate meshes.

Some details of the grid close to the leading and trailing edge

are also shown for Mod 3 mesh.

Fig. 8 Airfoil sub-grid mesh, Mod 4

V.SIMULATED FLOW CONDITIONSSimulations were performed using the commercial RANS

solver ANSYS FLUENT, which implements 2-D Reynolds-

averaged Navier-Stokes equations using a finite volume-finiteelement based solver. A segregated solver, implicit

formulation, was chosen for unsteady flow computation. The

fluid was assumed to be incompressible. As a global

convergence criterion, residuals were set to 10-5

.

VI. RESULTS AND DISCUSSIONTable V shows the DU91-W2-250 reference lift and drag

values, respectively defined as:

Cl = L / (cV2) (3)

Cd = D / (cV2) (4)

which were measured at Delft University Low-speed Wind

Tunnel [12] for an angle of attack of = 0.49 deg.

TABLEV

DU91-W2-250 REFERENCE LIFT AND DRAG VALUES MEASURED AT DELFT

UNIVERSITY LOW-SPEED WIND TUNNEL FOR =0.49 DEG (FROM:[12])

Denomination Value

Cl [-] 0.469

Cd [-] 0.00766

TABLEVI

NUMERICAL PREDICTED LIFT COEFFICIENT AND RELATIVE PERCENTAGE

DEVIATION WITH RESPECT TO EXPERIMENTAL MEASUREMENTS,SPALART-

ALLMARAS TURBULENCE MODEL

Denomination Cl [-] Cd [-]

Mod10.38176

(-18.6%)

0.01558

(+103.3%)

Mod20.42409

(-9.6%)

0.01298

(+69.5%)

Mod30.42691

(-9%)

0.01307

(+70.6%)

Mod40.42211

(-10%)

0.01331

(+73.8%)


917

8/2/2019 v63-173

5/8

Tables VI and VII show a comparison between computed

and measured lift and drag coefficients, as a function of the

adopted spatial discretization, for both Spalart-Allmaras

turbulence model and - Transitional model. It clearly

appears that Mod 3 and Mod4 grids determine the best results

in terms of percentage deviations from the experimentalmeasurements. Moreover, the prediction capabilities of the -

Transitional model appear to be quite higher with respect to

the Spalart-Allmaras turbulence model, as far as drag

prediction is concerned.

TABLEVII

NUMERICAL PREDICTED LIFT COEFFICIENT AND RELATIVE PERCENTAGE

DEVIATION WITH RESPECT TO EXPERIMENTAL MEASUREMENTS,-

TRANSITIONAL MODEL

Denomination Cl [-] Cd [-]

Mod10.31888

(-32%)

0.01633

(+113.3%)

Mod2 0.3367(-28.3%)

0.01409(+83.9%)

Mod30.44596

(-4.9%)

0.00886

(+15.7%)

Mod40.44381

(-5.4%)

0.00908

(+18.5%)

Fig. 9 Graphical representation of the distribution of the y+ parameter

along blade pressure and suction sides; Mod1 mesh, Spalart-Allmaras

turbulence model

Figs. from 9 to 16 show the distribution of the y+

parameter

along both airfoil pressure and suction sides for the four

candidate grid architectures.

A statistical procedure was created with the aim of

determining the optimal distribution of the y+

along the airfoil:

a global interval [0;1000] was considered for the y+

parameter,

then the sub-interval [0;8] was subdivided into a series of steps

of 0.25, while all values between 8 and 1000 were picked up

together.

The probability for the y+

value, at any given point along the

airfoil, to be comprised inside each sub-interval was defined

as:

p = Y/X (5)

being X the number of grid elements having the y+

comprised

in the considered interval and Y the total number of grid

elements on airfoil pressure/suction side.

Fig. 10 Graphical representation of the distribution of the y+

parameter along blade pressure and suction sides; Mod2 mesh,

Spalart-Allmaras turbulence model




The higher quality of Mod 3 grid spacing, confirmed by the

good results obtained by the computation of the aerodynamic

coefficients, clearly appears from the distribution of the

relative y+

parameter between the prescribed values 1y+5.

The use of the proposed statistical methodology for the

analysis of the quality of the grid is independent from the

tested airfoil geometry or angle of attack and could be

generalized for the whole polar of the considered airfoil.


918

8/2/2019 v63-173

6/8

Further work should be performed, in order to numerically

determine the whole range of lift and drag coefficients for the

considered airfoil geometry, as a function of the angle of

attack.




Fig. 13 Graphical representation of the distribution of the y

+

parameter along blade pressure and suction sides; Mod1 mesh, -

Transitional model

Finally, once Mod 3 mesh was identified as the better spatial

discretization, the distribution of the skin friction coefficient

along both airfoil pressure and suction sides was investigated.

Figs. 17 and 18 show a comparison between the numerical

predicted skin friction drag using both Spalart-Allmaras

turbulence model and - Transitional model. As can be

clearly seen, the Spalart-Allmaras turbulence model is unable

to predict the laminar to turbulent transition, which is

registered by the - Transitional model (evidenced by the

green arrows) for nearly 35% of chord length.

The registered drag overestimation (+70.6%) of the Spalart-

Allmaras turbulence model is connected to the overprediction

of the skin friction drag due to a fully turbulent simulation of

the flow field close to the airfoil, being the area under the skin

friction curve equal to the overall skin friction coefficient. The

described phenomenon is quite relevant for the airfoil pressureside, as evidenced by the orange arrows in Fig. 18.



Transitional model



Transitional model

VII.CONCLUSIONS AND FUTURE WORKSLaminar to turbulent transition on the DU91-W2-250 airfoil

was investigated by means of a CFD simulation of the flow

field using the - Transitional model. Numerical results were

compared to both wind tunnel experimental measurements and

Spalart-Allmaras turbulence model predictions.

A significant improvement in drag prediction was obtained

by using the transitional computation (15.7% overestimation)

in comparison with the fully turbulent simulation (70.6%

overestimation). The analysis of the distribution of the skin

friction coefficient along the airfoil pressure and suction sides

confirmed the - Transitional model capability of foreseeing


919

8/2/2019 v63-173

7/8

the laminar to turbulent transition which, for the present case,

was estimated at 35% of the chord length.

Fig. 16 Graphical representation of the distribution of the y

+


Transitional model

Fig. 17 Numerical predicted skin friction coefficient at suction side

for Mod 3 mesh using both Spalart-Allmaras turbulence model and - Transitional model (the green arrow evidences the point of laminar

to turbulent transition onset)

Fig. 18 Numerical predicted skin friction coefficient at pressure side

for Mod 3 mesh using both Spalart-Allmaras turbulence model and -

Transitional model (the green arrow evidences the point of laminar

to turbulent transition onset, while the orange arrows evidence the

deep differences in skin friction drag prediction between Spalart-

Allmaras turbulence model and - Transitional model)

Finally, grid quality was investigated by means of a

statistical methodology, obtained by subdividing the global y+

range in several sub-intervals and computing the probability of

the y+

value at any given point along the airfoil to be

comprised inside each sub-interval.

Further work should be performed, in order to extend thepresent analysis to a wider range of angles of attack.

NOMENCLATURE

c [m] chord length

Cd [-] drag coefficient

Cl [-] lift coefficient

cf[-] skin friction coefficient

D [N] drag force acting on the airfoil

L [N] lift force acting on the airfoil

P [-] probability for the y+

value at any given point

along the airfoil to be comprised inside each

sub-intervalRe [-] airfoil Reynolds number

u [m/s] tangential wall velocity

Vx [m/s] free-stream wind velocity, x-component

Vy [m/s] free-stream wind velocity, y-component

V[m/s] free-stream wind velocity

x [m] curvilinear coordinate along airfoil

suction/pressure side

X [-] number of grid elements having the y+

comprised in the considered interval

y [m] wall-grid centroid distance

y+

[-] wall y-plus

Y [-] total number of grid elements on airfoil

pressure/suction side

[deg] airfoil angle of attack

[Pas] dynamic viscosity

[kg/m3] air density

w [N/m2] wall shear stress

REFERENCES

[1] European Wind Energy Association, EU energy policy after 2020,www.ewea.org, 2011.

[2] M. Raciti Castelli, G. Grandi and E. Benini, Numerical Analysis of thePerformance of the DU91-W2-250 Airfoil for Straight-Bladed Vertical-

Axis Wind Turbine Application, submitted to ICAFM 2012:

International Conference on Advances in Fluid Mechanics, Florence

(Italy), February 28-29, 2012.[3] W.A. Timmer, W. A. and R. P. J. O. M. van Rooij, Summary of the

delft university wind turbine dedicated airfoils,AIAA-2003-0352.

[4] W.A. Timmer, W. A. and R. P. J. O. M. van Rooij, Design of airfoilsfor wind turbine blades, DUWIND, section Wind Energy, Faculty

CiTG, 03 May, 2004.

[5] G. Lombardi, M. V. Salvetti and D. Pinelli, Numerical Evaluation ofAirfoil Friction Drag,J. Aircraft, Vol. 37, No. 2, pp. 354-356, 2000.

[6] Y. Lian and W. Shai, Laminar-Turbulent Transition of a Low ReynoldsNumber Rigid or Flexible Airfoil, AIAA Journal, Vol. 45, No. 7, July

2007, pp. 1501-1513.

[7] F. R. Menter, R. B. Langrty, S. R. Likki, Y. B. Suzen, P. G. Huang andS. Vlker, A Correlation-Based Transition Model Using Local

Variables Part I: Model Formulation, Journal of Turbomachinery,

Volume 128, Issue 3, pp. 413-422, 2006.

[8] F. R. Menter, R. B. Langrty, S. R. Likki, Y. B. Suzen, P. G. Huang andS. Vlker, A Correlation-Based Transition Model Using Local


920

8/2/2019 v63-173

8/8

Variables Part II: Test Cases and Industrial Applications, Journal of

Turbomachinery, Volume 128, Issue 3, pp. 423-434, 2006.

[9] E. Benini and R. Ponza, Laminar to Turbulent Boundary LayerTransition Investigation on a Supercritical Airfoil Using the -

Transitional Model, 40th

Fluid Dynamics Conference and Exhibit, 28

June 1 July 2010, Chicago, Illinois, AIAA 2010-4289.

[10]

S. Hosseinverdi and M. Boroomand, Prediction of Laminar-TurbulentTransitional Flow over Single and Two-Element Airfoils, 40th Fluid

Dynamics Conference and Exhibit, 28 June 1 July 2010, Chicago,

Illinois, AIAA 2010-4290.

[11] L. Yuhong and L. Congming, A numerical simulation of flow around awind turbine airfoil based on transition model, WNEC 2009: World

Non-Grid-Connected Wind Power and Energy Conference, Nanjing

(China), 24-26 Sept. 2009.

[12] W.A. Timmer, W. A. and R. P. J. O. M. van Rooij, Aifoil DU91-W2-250 Coordinates and Measurements in Delft University 1.25x1.80 m

Low-speed Wind tunnel, data provided by direct contact from the

authors.

[13] ANSYS FLUENT 12.0-12.1 Documentation, Release 12.1 ANSYS,Inc. 2009-10-01.

[14] J. Johansen, Prediction of Laminar/Turbulent Transition in AirfoilFlows, Ris National Laboratory, Roskilde, Denmark, May 1997,

Ris-R-987(EN).

[15] M. Raciti Castelli, F. Garbo, E. Benini, Numerical investigation oflaminar to turbulent boundary layer transition on a NACA 0012 airfoil

for vertical-axis wind turbine applications, Wind Engineering, Vol. 35,

No. 6, 2011, pp. 661-686.


921

v63-173

Documents

Transcript of v63-173